Hopf Bifurcation of the Higher Dimensional Hénon Map

Abstract

In this paper, the discrete time generalized Hénon map is considered and the existence of Hopf bifurcation via an explicit
criterion for , in particular for has given. The relation between the parameters and as well as
the range of the values of the parameters for has driven and the existence of Hopf bifurcation is demonstrated
for the values of the parameters calculated from their relations. The results of numerical simulations for different values of
the parameters are also presented.